How to Find GCF of 2/20, 75/749, 17/821?

GCF of 2/20, 75/749, 17/821

Created By : Veerendra
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023

Use our free GCF of Fractions Calculator tool to compute the GCF of 2/20, 75/749, 17/821 i.e 1/12298580 easily. The following is the detailed procedure to determine the greatest common factor of fractions 2/20, 75/749, 17/821.

Enter two or more fractions separated by "commas"

Ex: 2/3, 5/7 or 3/5, 5/9, 7/3

What is the GCF of 2/20,75/749,17/821?

Given fractions are 2/20,75/749,17/821

To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by

GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators

In the fractions 2/20,75/749,17/821, numerators are 2,75,17

Denominators are 20,749,821

The GCF of 2,75,17 is 1 .

LCM of 20,749,821 is 12298580.

The greatest common factor of 2/20,75/749,17/821 = [GCF of 2,75,17]/[LCM of 20,749,821]= 1/12298580

Therefore, the GCF of 2/20,75/749,17/821 is 1/12298580.

Greatest Common Factor of 2,75,17

To find the highest common factor of 2,75,17, we have to find the factors of both numbers and list the highest common factor.

The factors of 2 are 1, 2

The factors of 75 are 1, 3, 5, 15, 25, 75

The factors of 17 are 1, 17

The HCF of 2,75,17 is 1.

Lets's calculate GCF of 2,75,17

Greatest Common Factor (GCF) of 2,75,17 By Common Division

∴ So GCF of numbers is 1 because of no common factors present between them.

Greatest Common Factor of 2,75,17 By Matching Biggest Common Factor Method

Now, list down the factors of 2

1,2

Now, list down the factors of 75

1,3,5,15,25,75

Now, list down the factors of 17

1,17

Greatest Common Factor

We found the factors 2,75,17 . The biggest common factor number is the GCF number.
So the greatest common factor 2,75,17 is 1.

Lets's calculate LCM of 20,749,821

Lowest Common Multiple of 20,749,821 using Common Division

Given numbers has no common factors except 1. So, there LCM is their product i.e 12298580

Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/12298580

Therefore, the GCF of Fractions 2/20,75/749,17/821 is 1/12298580

Least Common Multiple of 20,749,821 with GCF Formula

The formula of LCM is LCM(a₁,a₂,a₃....,a_n) = ( a₁ × a₂ × a₃ × .... × a_n) / GCF(a₁,a₂,a₃....,a_n) x common factors(if more than 2 numbers have common factors).

We need to calculate greatest common factor of 20,749,821 and common factors if more than two numbers have common factor, than apply into the LCM equation.

GCF(20,749,821) = 1

common factors(in case of two or more numbers have common factors) = 1

GCF(20,749,821) x common factors =1 x 1 = 1

LCM(20,749,821) = ( 20 × 749 × 821 ) / 1

LCM(20,749,821) = 12298580 / 1

LCM(20,749,821) = 12298580

GCF of Fractions Calculation Examples

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FAQs on GCF of Fractions of 2/20, 75/749, 17/821

1. What is the HCF of 2,75,17?

The HCF of 2,75,17 is 1

2. What is the GCF of a fraction?

The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.

3. How to find GCF in Fractions?

Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.

4. What is the GCF of Fractions for 2/20, 75/749, 17/821?

Answer: GCF of Numerators as per given numbers 2/20, 75/749, 17/821 is

GCF of Numerators i.e. for 2,75,17 is 1

LCM of denominators i.e. for 20,749,821 is 12298580.

Thus, GCF of Fractions is 1/12298580.Finally, GCF of Fractions for 2/20, 75/749, 17/821 is 1/12298580.